GIS is the critical equipment in the substation; the internal temperature distribution can effectively reflect the operating conditions of the equipment, but there is a lack of accurate online monitoring of the internal temperature rise of GIS methods and means. Since it is impossible to forecast in advance, the present methods can frequently only infer the presence of thermal faults inside the GIS when there is a clear anomalous temperature rise in the enclosure. Thus, we first present a transient temperature rise equilibrium mathematical model of the GIS busbar enclosure based on the temperature gradient in this work, and we investigate the evolution characteristics of the equilibrium coefficients with the temperature and the temperature gradient. Next, a method based on transient temperature rise monitoring of the enclosure is provided to detect anomalous temperature rise in conductors. Finally, the temperature rise tests under different external ambient temperatures and load currents are carried out to obtain the transient temperature evolution of the ambient environment, enclosure, and conductor. The test results indicate that the absolute value of the equilibrium co-efficient varies monotonically at different external ambient temperatures and load currents. The interior conductor temperature rise rate can be perceived by observing the GIS busbar enclosure"s transient temperature rise. This article offers a technical method for using exterior temperature monitoring to track the interior temperature rising status of the GIS busbar.